Can I ask for her office?

I have been at my job for a month. After being here for a week a co-worker quit. Although we are the same level, she had been here 12 years.
When I interviewed I was told I would have an office, instead when I started my desk was put in a reception area due to lack of space.
How do I approach the new boss (while being tactful) that I would like the quitters office?

More than likely they have a plan for this office already. Someone has probably already beat you to the punch by lining up this office for themselves. What I would do is to ask around and see if anyone else knows about this office and what is going to be done with it.
When you do go to your boss about this office you should come up with some good reasons why it would be important for you to have an office. Do you recieve phone calls in which confidentiality would be important? Do you think that this office would increase your productivity? Do you have the space requirements that would merit an office?
Really what you gotta do is show that you have a need for the office and not just a want.

Just ask if it is available as you were told you would have an office. If you dont ask you dont get.

Just ask. At my job it's no big deal. Why are you so scared to ask? It's just an office and a desk. If they say no, they say no. They shouldn't care that you inquired.

If you don't ask, someone else WILL and get it.